So, it would be possible to not make estimated tax payments at all so long as a couple just writes the check at the end?

As the late, great Katherine Kuhlman was fond of noting, "Anything is possible with God."

Nothing has changed about prepayment rules, which cover everything on the 1040. Estimated tax payments are one method for avoiding an underpayment penalty. There are others, all of which are covered in detail in Pub 505.